Question: $A$ $B$ $C$ If: $ AC = 18$, $ BC = 6x + 5$, and $ AB = 5x + 2$, Find $BC$.
From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {5x + 2} + {6x + 5} = {18}$ Combine like terms: $ 11x + 7 = {18}$ Subtract $7$ from both sides: $ 11x = 11$ Divide both sides by $11$ to find $x$ $ x = 1$ Substitute $1$ for $x$ in the expression that was given for $BC$ $ BC = 6({1}) + 5$ Simplify: $ {BC = 6 + 5}$ Simplify to find ${BC}$ : $ {BC = 11}$